When machining or otherwise processing plate-shaped workpieces, a handling device can be used to feed unmachined raw workpieces for processing and/or to remove workpieces produced as processed products. An example of such a handling device may be found in EP 1 967 301 A1, which describes a handling device with a sucker frame that can be raised and lowered and can also be moved in a horizontal direction. Provided on the sucker frame are a total of four removal bars which, on the workpiece side, are provided with suckers for fixing the products that are to be handled. The removal bars form bearing structure segments of a bearing structure composed of the removal bars. The planar extent of the bearing structure is variable. For this purpose, two of the removal bars can be jointly positioned linearly relative to the two other removal bars by a controlled motor drive. This positioning option is used to adapt the bearing structure, formed by the removal bars, and thereby particularly also the configuration of the suction field, consisting of the suckers of the removal bars, of the bearing structure, to different conditions of use.